You should be able to 'resurrect' your JAR licence to an EASA version with not too much drama. Also give thought to the effect that Brexit will have on UK issued licences, as it will affect individuals in different ways, depending on how they wish to use their licence. More info here:
UK CAA - Brexit - Private Pilots
A quick phone call or an email to an approved training organisation should be able to provide some clarity for what you would need to do.